TY - JOUR
T1 - Tuning Cooperative Behavior in Games with Nonlinear Opinion Dynamics
AU - Park, Shinkyu
AU - Bizyaeva, Anastasia
AU - Kawakatsu, Mari
AU - Franci, Alessio
AU - Leonard, Naomi Ehrich
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2022
Y1 - 2022
N2 - We examine the tuning of cooperative behavior in repeated multi-agent games using an analytically tractable, continuous-time, nonlinear model of opinion dynamics. Each modeled agent updates its real-valued opinion about each available strategy in response to payoffs and other agents' opinions, as observed over a network. We show how the model provides a principled and systematic means to investigate behavior of agents that select strategies using rationality and reciprocity, key features of human decision-making in social dilemmas. For two-strategy games, we use bifurcation analysis to prove conditions for the bistability of two equilibria and conditions for the first (second) equilibrium to reflect all agents favoring the first (second) strategy. We prove how model parameters, e.g., level of attention to opinions of others, network structure, and payoffs, influence dynamics and, notably, the size of the region of attraction to each stable equilibrium. We provide insights by examining the tuning of the bistability of mutual cooperation and mutual defection and their regions of attraction for the repeated prisoner's dilemma and the repeated multi-agent public goods game. Our results generalize to games with more strategies, heterogeneity, and additional feedback dynamics, such as those designed to elicit cooperation or coordination.
AB - We examine the tuning of cooperative behavior in repeated multi-agent games using an analytically tractable, continuous-time, nonlinear model of opinion dynamics. Each modeled agent updates its real-valued opinion about each available strategy in response to payoffs and other agents' opinions, as observed over a network. We show how the model provides a principled and systematic means to investigate behavior of agents that select strategies using rationality and reciprocity, key features of human decision-making in social dilemmas. For two-strategy games, we use bifurcation analysis to prove conditions for the bistability of two equilibria and conditions for the first (second) equilibrium to reflect all agents favoring the first (second) strategy. We prove how model parameters, e.g., level of attention to opinions of others, network structure, and payoffs, influence dynamics and, notably, the size of the region of attraction to each stable equilibrium. We provide insights by examining the tuning of the bistability of mutual cooperation and mutual defection and their regions of attraction for the repeated prisoner's dilemma and the repeated multi-agent public goods game. Our results generalize to games with more strategies, heterogeneity, and additional feedback dynamics, such as those designed to elicit cooperation or coordination.
KW - Game theory
KW - decision making
KW - distributed control
KW - multi-agent systems
KW - opinion dynamics
UR - http://www.scopus.com/inward/record.url?scp=85122316796&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85122316796&partnerID=8YFLogxK
U2 - 10.1109/LCSYS.2021.3138725
DO - 10.1109/LCSYS.2021.3138725
M3 - Article
AN - SCOPUS:85122316796
SN - 2475-1456
VL - 6
SP - 2030
EP - 2035
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
ER -